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In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?
- a)The system undergoes a phase transition from a solid to a liquid phase.
- b)The system undergoes a phase transition from a liquid to a solid phase.
- c)The number of particles in the system increases as the chemical potential is increased.
- d)The number of particles in the system decreases as the chemical potential is increased.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In the grand canonical ensemble, which of the following statements is ...
In the grand canonical ensemble, the chemical potential μ is a key parameter that controls the number of particles in the system.
When the chemical potential is high, it is energetically unfavorable to add more particles to the system, so the number of particles is small.
Conversely, when the chemical potential is low, it is energetically favorable to add more particles to the system, so the number of particles is large.
Therefore, as the chemical potential is increased, the number of particles in the system decreases.
Options A and B are incorrect as they describe a phase transition between solid and liquid phases, which may occur as a result of changes in temperature or pressure, but not necessarily due to changes in chemical potential.
Option C is incorrect as it states that the number of particles increases as the chemical potential is increased, which is the opposite of what happens in the grand canonical ensemble.
When the chemical potential is high, it is energetically unfavorable to add more particles to the system, so the number of particles is small.
Conversely, when the chemical potential is low, it is energetically favorable to add more particles to the system, so the number of particles is large.
Therefore, as the chemical potential is increased, the number of particles in the system decreases.
Options A and B are incorrect as they describe a phase transition between solid and liquid phases, which may occur as a result of changes in temperature or pressure, but not necessarily due to changes in chemical potential.
Option C is incorrect as it states that the number of particles increases as the chemical potential is increased, which is the opposite of what happens in the grand canonical ensemble.
Most Upvoted Answer
In the grand canonical ensemble, which of the following statements is ...
Explanation:
The grand canonical ensemble is a statistical ensemble used to describe a system in equilibrium with a reservoir of particles, energy, and volume. In this ensemble, the chemical potential (μ) is varied to control the number of particles in the system.
Statement: The number of particles in the system decreases as the chemical potential is increased.
Explanation:
When the chemical potential is increased, it means that the system is in contact with a reservoir with a higher chemical potential. This implies that there is a higher probability for particles to enter the system from the reservoir than to leave the system and enter the reservoir.
Key Points:
- The chemical potential represents the energy required to add or remove a particle from the system.
- When the chemical potential is increased, the energy required to add a particle to the system is higher than before.
- This higher energy requirement makes it less favorable for particles to enter the system.
- As a result, the number of particles in the system decreases as the chemical potential is increased.
Conclusion:
Therefore, in the grand canonical ensemble, the number of particles in the system decreases as the chemical potential is increased. This is because the higher energy requirement for particle addition makes it less likely for particles to enter the system from the reservoir.
The grand canonical ensemble is a statistical ensemble used to describe a system in equilibrium with a reservoir of particles, energy, and volume. In this ensemble, the chemical potential (μ) is varied to control the number of particles in the system.
Statement: The number of particles in the system decreases as the chemical potential is increased.
Explanation:
When the chemical potential is increased, it means that the system is in contact with a reservoir with a higher chemical potential. This implies that there is a higher probability for particles to enter the system from the reservoir than to leave the system and enter the reservoir.
Key Points:
- The chemical potential represents the energy required to add or remove a particle from the system.
- When the chemical potential is increased, the energy required to add a particle to the system is higher than before.
- This higher energy requirement makes it less favorable for particles to enter the system.
- As a result, the number of particles in the system decreases as the chemical potential is increased.
Conclusion:
Therefore, in the grand canonical ensemble, the number of particles in the system decreases as the chemical potential is increased. This is because the higher energy requirement for particle addition makes it less likely for particles to enter the system from the reservoir.
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In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer?.
In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer?.
Solutions for In the grand canonical ensemble, which of the following statements is true about the behavior of the system as the chemical potential is varied?a)The system undergoes a phase transition from a solid to a liquid phase.b)The system undergoes a phase transition from a liquid to a solid phase.c)The number of particles in the system increases as the chemical potential is increased.d)The number of particles in the system decreases as the chemical potential is increased.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UGC NET.
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